Formula Sheet Downloads
- Formula Sheets
- Coherence Formula Sheet
- HRV Formula Sheet
- Breathing From ACC Formula Sheet
- Breathing Dynamics Formula Sheet
Primary Sources
Polar BLE SDK (MIT License) Repository: https://github.com/polarofficial/polar-ble-sdk Technical documentation (tag 4.0.0): https://github.com/polarofficial/polar-ble-sdk/tree/4.0.0/technical_documentation/
The SDK's open-source code and technical documentation provide the authoritative reference for the Polar Measurement Data (PMD) service protocol, including measurement type identifiers, control point command structures, and data frame encoding formats.
Polar Measurement Data Specification for 3rd Party (PDF) Published by Polar Electro. This document describes the PMD service interface for third-party developers. It is referenced here for protocol comprehension; content in this repository's documentation is written independently.
SieciĆski, S.; Kostka, P.S.; Piaseczna, N.J.; Janik, S.; Delgado-Prieto, M.; Boczar, T. "The Newer, the More Secure? Comparing the Polar Verity Sense and H10 Heart Rate Sensors." Sensors 2025, 25, 2005. https://doi.org/10.3390/s25072005
This paper evaluates the Polar H10 and Verity Sense in terms of data quality and measurement reliability, providing independent validation of ECG and accelerometer data characteristics.
McCraty, R.; Atkinson, M.; Tomasino, D.; Bradley, R.T. The Coherent Heart: Heart-Brain Interactions, Psychophysiological Coherence, and the Emergence of System-Wide Order. Institute of HeartMath, Publication No. 06-022, 2006.
This monograph provides the spectral coherence ratio used by the app's RR-derived coherence workflow: search the dominant peak in
0.04-0.26 Hz, integrate a0.030 Hzpeak window, and compare it against total power in0.0033-0.4 Hz.Real-session note: the app consumes RR intervals from the Heart Rate Measurement characteristic, while the physical H10 derives those beat intervals from ECG timing inside the strap.
Short-Term HRV Source
Shaffer, F.; Ginsberg, J. P. "An Overview of Heart Rate Variability Metrics and Norms." Front. Public Health 5:258, 2017. https://doi.org/10.3389/fpubh.2017.00258
This paper is the short-term HRV reference for the app's HRV tab. The tab defaults to a
300 sRR window, usesRMSSDas the headline value, and keepsSDNN,pNN50,SD1,mean NN,mean HR, andlnRMSSDvisible as supporting telemetry.The repository intentionally treats these values as short-term RR-derived telemetry, not as a substitute for
24 hnorms or full clinical artifact correction.Synthetic-session note: the sibling
SyntheticBioharness now emits PMD ECG frames that stay synchronized with the same synthetic RR schedule used for coherence and HRV warmup, so synthetic operator tests keep the waveform and interval views aligned even though breathing still bypasses PMD ACC.
Breathing Dynamics Sources
Goheen, D. P.; et al. "It's About Time: Breathing Dynamics Modulate Emotion and Cognition." Psychophysiology 2025. https://doi.org/10.1111/psyp.70149
This paper defines the breathing-dynamics feature family used by the app's breathing-dynamics window: breath interval and breath amplitude series plus mean, standard deviation, coefficient of variation, autocorrelation window, PSD slope, Lempel-Ziv complexity, sample entropy, and multiscale entropy.
CANALLAB / breathing_wm https://github.com/CANALLAB/breathing_wm
The paper links this repository as the companion analysis code for the published workflow. It is included here as method provenance only; this repo does not embed that code directly.
NeuroKit2 implementation references
- sample entropy: https://neuropsychology.github.io/NeuroKit/_modules/neurokit2/complexity/entropy_sample.html
- multiscale entropy: https://neuropsychology.github.io/NeuroKit/_modules/neurokit2/complexity/entropy_multiscale.html
- PSD slope: https://neuropsychology.github.io/NeuroKit/_modules/neurokit2/complexity/fractal_psdslope.html
- autocorrelation: https://neuropsychology.github.io/NeuroKit/_modules/neurokit2/signal/signal_autocor.html
- Lempel-Ziv complexity: https://neuropsychology.github.io/NeuroKit/_modules/neurokit2/complexity/complexity_lempelziv.html
Goheen et al. explicitly state that these feature families were computed with NeuroKit2. Where the paper leaves entropy hyperparameters unspecified, this repository documents explicit defaults and keeps them close to that implementation path.
Breathing Dynamics Provenance Note
The breathing-dynamics runtime in this repository is an adaptation, not a claim
of numeric identity with the paper's respiration-belt pipeline. Goheen et al.
derive their breath interval and amplitude series from a preprocessed belt
signal; this app derives the same feature family from the calibrated ACC-based
breathing waveform already available in PolarBreathingTracker.
The app's default entropy settings are explicit and operator-visible:
- SampEn:
m=2,delay=1,r=0.2 * SD - MSE:
m=3,delay=1,r=0.2 * SD, scales1..5, summary=AUC
Those defaults are intended to stay aligned with the NeuroKit2 path cited by the paper while making the runtime behavior reproducible inside this repository.
The current runtime also suppresses undefined entropy solves instead of inventing a finite fallback value, and its PSD slope path now follows the NeuroKit2-style detrend plus low-frequency log-log fit more closely.
Breathing From ACC Provenance Note
The ACC breathing-volume tracker in this repository is repo-specific code. It is documented as an approximation rather than a validated published method.
Current status:
- it has not yet been externally validated
- a validation study is actively being worked on
Bluetooth SIG Specifications
- Heart Rate Service (Service UUID
0x180D): Bluetooth SIG Assigned Numbers and GATT Specification Supplement. - Heart Rate Measurement Characteristic (
0x2A37): Format defined in the GATT Specification Supplement, Section 3.106. - Client Characteristic Configuration Descriptor (
0x2902): Defined in the Bluetooth Core Specification, Vol 3, Part G, Section 3.3.3.3.
License Note
This repository is an independent implementation. Protocol knowledge was derived from the sources above, the Polar BLE SDK's MIT-licensed code, and direct BLE traffic analysis. No proprietary Polar documentation is reproduced verbatim.